In the treatment of arterial hypertension, the optimal reduction in blood pressure is obviously the one that causes the maximum achievable prevention of hypertension-associated cardiovascular morbidity and mortality. This goal has clearly not been reached by today's approach to the treatment of elevated blood pressure. Treated hypertensive patients are still at increased risk of cardiovascular morbidity and mortality in spite of receiving antihypertensive treatment, as shown in many intervention studies. One possible explanation for this outcome could be that treated blood pressure is rarely brought down to strictly normotensive levels, again as shown in numerous studies. This finding would suggest that a more vigorous lowering of blood pressure would be advantageous when treating hypertensive patients. On the other hand, the fact that the relationship between the level of blood pressure and risk is J-shaped obviously means that vigorous lowering of blood pressure may increase cardiovascular risks, if blood pressure is brought down too far. Several open, retrospective, nonrandomized studies have been analyzed with this issue in mind, but so far only two prospective intervention trials have been specifically designed to address this problem: the BBB Study, published in 1994, and the much larger HOT Study, published in 1998. The rationale of these studies as well as some of their findings will be discussed briefly here, with emphasis on the HOT Study.